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Course: Algebra 2>Unit 2

Lesson 4: Adding and subtracting complex numbers

Subtracting complex numbers

Learn how to break down the process of subtracting complex numbers into simple steps. Distribute the negative sign to get rid of parentheses, then add up the real and imaginary parts separately. Voila! You've got your answer in the form of a + bi. Created by Sal Khan and Monterey Institute for Technology and Education.

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• I still don't know which part is imaginary and which part is real. Can someone explain it to me?
• in a complex number a + bi, a is the real part, and bi is the imaginary part, with b not equal to 0.

e.g. 5 + 2i, 5 is real, 2i is imaginary.
6 - 3i, 6 is real, 3i is imaginary. (or -3i, if you like.)

hope this helps!
• Imaginary numbers are so simple yet complex
• Why imaginary number is called imaginary number................
• "Those numbers were once poorly understood and regarded by some as fictitious.The use of imaginary numbers was not widely accepted by many .It was left to Euler and others to use them. Euler, in his wrote in his Introduction to Algebra
Because all conceivable numbers are either greater than zero or less than 0 or equal to 0, then it is clear that the square roots of negative numbers cannot be included among the possible numbers [real numbers]. Consequently we must say that these are impossible numbers. And this circumstance leads us to the concept of such number, which by their nature are impossible, and ordinarily are called imaginary or fancied numbers, because they exist only in imagination.
In short, it is a matter of acceptance of or the lack of it which gave them the name."
• So in adding, subtracting, and multiplying the imaginary unit i, we are literally just treating it like a variable?
• For the most part. The exception is multiplication.
-- If you have a problem that requires that you multiply i*i, you need to change it to -1.
-- If you have "i" with an exponent, you can do the multiplication.

Hope this helps.
• Is this really this simple?( I mean are there more sophisticated problems?)
• I think the aim here is to make you understand the concept..
if you want more 'sophisticated' problems, you should try buying a book or searching on the web for them
• How would one solve a problem like:
(-4-√ 75)/40
or one like:
5/(7-i)
Is there a video for these types of problems?
• How do you distribute the minus sign when subtracting complex numbers?
• Hello Sam, you can treat a complex number like any other pair of numbers. Example: -(6+18i) becomes, -6-18i. Similarly, -(-5-24i) becomes 5+24i. An easy way to think about it is to sperate the numbers, -(6+18i) is the same as: -(6)+ -(18i). For pairs it is the same. (24+5i)-(15-12i) can be re-written as: (24+5i)+(-15+12i). Hope this helps!
• how do you do the problem (1+5)-7-(8i)
• 1+5=6
6-7=-1
-(8i)=-8i
so -1-8i